you are looking at dividing the definite integral of f(x) from 0 to 5 by the length of the interval, namely (5-0)=5.
∫(1/5)exdx
=(1/5)[ex] from 0 to 5
=(1/5)(e5-e0)
=(1/5)(148.413-1)
=29.483
The average over the interval
=29.483/5
=5.8965

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